Robust Optimization Design For Control Systems With Finite Frequency Specifications

Design specifications for practical dynamical systems control synthesis are often given in terms of a series of frequency domain inequalities. These inequalities are defined in the entire frequency range or finite frequency ranges. Robust optimization design of control systems with such specifications is one of important research subjects for control theory and a great number of research results have been reported, but there are still some problems to be solved. For example, for robust mixed frequency (that is the entire fre-quency and finite frequency) multi-objective control of linear systems, the following two approaches can be obtained from the existing results:use weighting functions to achieve finite frequency range restriction then adopt the entire frequency approaches to deal with, and it will bring inaccuracy; see the entire frequency specifications as a special case of fi-nite frequency ones then adopt finite frequency approaches based on the generalized KYP lemma to deal with, and it will bring conservatism. For fault-tolerant control of linear systems and finite frequency single-objective synthesis of linear time-delay systems, the existing results, ignoring the finite frequency character of disturbances (including stuck fault signals for fault-tolerant control) and extending finite frequency specifications to the entire frequency range, adopted directly the entire frequency approaches to deal with, and were obviously quite conservative.This thesis, based on the existing results, proposes mixed frequency approaches by combining the entire frequency results with finite frequency ones based on the general-ized KYP lemma for robust mixed frequency multi-objective control of linear systems, which avoid the inaccuracy produced by using weighting functions and the conservatism produced by reducing the finite frequency results to the entire frequency case; for fault-tolerant control of linear systems, gives design methods of fault-tolerant controllers based on the above-mentioned mixed frequency approaches, and accurately describes the re-jection performance in finite frequency ranges of stuck fault signals and disturbances; for finite frequency single-objective synthesis of linear time-delay systems, gives finite frequency approaches based on the generalized S-procedure, and it will reduce the con- servatism.The main contributions are as follows:Chapters1-2first summarize and analyze the development and main research meth-ods in research fields of finite frequency specifications, fault-tolerant control and time-delay systems. Preliminaries about the considered problems are also given.Chapter3considers the control synthesis problems via state feedback and dynamic output feedback for linear continuous-time systems with small gain specifications in mixed frequency ranges. The proposed controller design methods guarantee that the re-sulting closed-loop systems are asymptotically stable and meet the requirements of small gain specifications in both the entire frequency range and finite frequency ranges. The finite frequency small gain control synthesis conditions accurately restrict the frequency ranges of the corresponding disturbances; the entire frequency small gain control syn-thesis conditions avoid introducing additional conservatism. Simulations illustrate the advantages of our methods compared with the existing techniques.Chapter4considers the reliable H∞control synthesis problems via state feedback and dynamic output feedback for linear continuous-time systems. For the general actua-tor fault model including partial fault, outage and stuck fault cases, by characterizing the disturbance rejection performance of the stuck signal as zero-frequency small gain con-dition, the design methods of reliable H∞state feedback and dynamic output feedback controllers are presented, respectively, based on the mixed frequency small gain state feedback control approach in Chapter3and a two-step algorithm. Simulation examples illustrate the advantages of our methods compared with the existing approaches.Chapter5studies the adaptive fault-tolerant control synthesis problems via state feedback for linear continuous-time systems with actuator stuck faults and actuator partial faults. First, a design method of an adaptive fault-tolerant tracking controller is developed based on the online estimation of actuator stuck faults. In the event of actuator stuck faults, a compensation controller is incorporated into the initial controller to improve control effect and reject the zero-frequency disturbance produced by the stuck-actuators. Then, based on the online estimation of actuator partial faults, a design method of an adaptive fault-tolerant controller is obtained such that the resulting closed-loop systems, in both normal operation and fault cases, are asymptotically stable and satisfy finite fre-quency small gain conditions. It has been shown that the design conditions for adaptive controllers are more relaxed than those for the controllers with fixed gains, and simulation examples have illustrated the advantage of the proposed method. Chapter6studies the analysis and synthesis problems for linear multi-delay systems with finite frequency specifications. First, by virtue of the generalized S-procedure, the analysis condition of a finite frequency specification is presented. Then, the design meth-ods of finite frequency small gain state feedback controllers for the continuous-time case and of finite frequency small gain filters for the discrete-time case are given based on the analysis result, respectively. Numerical examples show the effectiveness of the proposed design methods by comparing with the existing techniques.Finally, the results of the dissertation are summarized and further research topics are pointed out.